Measurement and Simulation of Reflector Antenna L.J.Foged , M.A. Saporetti , M. Sierra-Castanner , E. Jorgensen , T. Voigt , F. Calvano , D. Tallini

Abstract— Well-established procedures are consolidated to II. MEASUREMENT CAMPAIGN determine the associated measurement uncertainty for a given antenna and measurements scenario [1-2]. Similar criteria for Comparative measurements based on high accuracy establishing uncertainties in numerical modelling of the same reference antennas and involving different antenna antenna are still to be established. In this paper, we investigate measurement systems are important instruments in the the achievable agreement between antenna measurement and evaluation, benchmarking and calibration of the measurement simulation when external error sources are minimized. The test facilities. Regular inter comparisons are also an important object, is a reflector fed by a wideband dual ridge horn (SR40-A instrument for traceability and quality maintenance. These and SH4000). The highly stable reference antenna has been activities promote and document the measurement confidence selected to minimize uncertainty related to finite manufacturing and material parameter accuracy. Two frequencies, 10.7GHz level among the participants and are an important prerequisite and 18GHz have been selected for detailed investigation. for official or unofficial certification of the facilities. Different European facility comparison campaigns, have The antenna has been measured in two reference spherical near-field measurement facilities as a preparatory activity for a been completed during the last years in the framework of Facility Comparison Campaign on this antenna in the frame of a different European Activities: Antenna Measurement Activity EurAAP/WG5 activity. A full CAD model, in step compatible of the Antenna Centre of Excellence-VT UE Frame Program; format, has been provided and the antenna has been simulated COST ASSIST, IC0603 and COST-VISTA, IC1102. using different numerical methods from different software Activities related to facility comparisons are now included vendors [4-7]. Each participant was responsible for generating a in the Antenna Measurement, Working Group 5 Activity of suitable mesh and the numerical stability of their solution. EurAAP, where a specific on-going task for Antenna Index Terms—antenna, measurement, simulation, numerical Measurement Intercomparison has been approved. methods.

I. TEST OBJECT The SR40-A and SH4000 antenna is shown in Fig. 1. The SR40-A is an offset parabolic reflector, precision machined from a single block of aluminum. The circular interface with precision holes allows the user to center the antenna with very high accuracy. The alignment accuracy is determined to within ±0.01°. The SH4000 wide band Dual Ridge Horn is a highly stable reference antenna. The antenna is precision fitted to the mounting bracket of the reflector. This antenna is selected as test object in a comprehensive measurement facility comparison activity as a EurAAP Working Group 5, activity. Fig. 1. Reflector SR 40-A fed by SH4000 Dual Ridge Horn: Antenna during measurement (Left); CAD file for simulation (Right). A. Test Plan and Participating Facilities • Description of numerical method (with illustration – The measured SR40-A and SH4000 antenna is part of a Ex: currents on reflector, grid used etc). currently ongoing larger measurement facility comparison A. GRASP (TICRA) campaign within a EurAAP Working Group 5 activity. Two spherical Near Field ranges, Technical University of Madrid GRASP offers a variety of analysis methods suitable for (UPM), Spain and SATIMO SG 64 (MVG), France, have electrically large scattering and radiation problems such as contributed to the reference measurements reported here. The reflector antennas and satellite platforms. The method used measurements data requested for the facility comparison here is a frequency domain higher-order Method of Moments campaign are reported in TABLE I. A full list of information surface integral equation solver using curved mesh elements up required from each participating facility, for the post to 2λ by 2λ. The solution is accelerated by a recently processing and the comparison of data, is reported in [3]. introduced Multi-level Fast Multipole Method (MLFMM) developed particularly for higher-order discretizations [14]. The new HO-MLFMM solver has been further enhanced with TABLE I. MEASUREMENT DATA, REFLECTOR SR 40-A FED BY SH4000 DUAL RIDGE HORN the ability to work with non-connected meshes, which provides increased robustness in practical applications. For the present 10.7, 12.6, 14.5,18, 19, 20, 28, 29, Frequency Range problem, the fine details of the feed was modelled with tiny Full 30, 31 ,33, 38 GHz 3D Phi From 0° to 135°(45° step) patches (0.01 λ) whereas the reflector surface was modelled Gain with large patches (2λ). The surface current was then expanded Measu Theta From -180° to 180° (1° step) in polynomials between 1st and 9th order depending on the rement Ports (K type Measurement: vertical electrical size of each patch. The MLFMM solver includes an female connectors) polarization efficient preconditioner that enables fast convergence while being rather insensitive to the presence of small geometrical B. Determination of Measured Reference Pattern details or the use of high polynomial orders. For the present 18 GHz example, a relative solution error of 0.001 was reached The access to measured data from different facilities in after 20 iterations. The currents induced on the antenna good agreement between them, increase the confidence level structure, as well as the mesh used in the computations, are of the measured data. shown in Fig.2. In [3], different data processing procedures have been investigated to derive reference patterns with increased confidence level based on measurements in different facilities. The reference pattern can be calculated as the simple mean or weighted mean of each measured data point where the weights are proportional to the estimated uncertainty. The uncertainty associated with the mean is “improved” if the measurements can be considered truly independent. For this activity, considering the availability of three sets of measurements data from UPM and MVG facilities, the simple mean of the radiation pattern, using amplitude data only, has been used to define the reference pattern.

III. SIMULATION CAMPAIGN Fig. 2. GRASP currents induced on the antenna and mesh grid @18GHz. Simulations have been performed at 10.7GHz and 18GHz, Reflector SR 40-and SH4000 fed (Left), Close-up of the feed (Right). considering the nominal dimensions of the feed and reflector and ignoring finite manufacturing and material parameter B. HFSS (ANSYS) accuracy. The electrical conductivity of aluminum was The currents induced on the structure for the present assumed to 3.56 107 S/m in the simulation of ohmic losses. problem at 10.7GHz and 18GHz are shown in Fig. 3. The complete CAD file of the antenna was provided to each of the participants involved. Each participant was responsible for generating a suitable mesh and the numerical stability of their solution. The information collected from simulations is reported below: • Peak directivity at 10.7 and 18 GHz; • Directivity patterns in 4 cuts (Ludwig III[8] Co/Cx 0º, 45º, 90º & 135º) -180º to 180º in 1º and 0.1º step; • Return loss; Fig. 3. HFSS simulated surface current density [email protected] (Left) and • Ohmic losses; 18GHz (Right) Reflector SR 40-A with SH4000 Dual Ridge Horn. The hybrid FEBI [9] is a powerful new enhancement to be used as an excitation source. The simulation of the reflector the FEM [13] solver available in HFSS. This new technique can be performed by the Integral Equation solver based on gives the design engineer the advantages of an FEM MLFMM or the Asymptotic Solver based on the Shooting and simulation with the efficiency and accuracy of an IE solution Bouncing Ray (SBR) method. Farfield results, generated using for open boundary problems. This procedure is accurate for this approach, agree very closely with the full time domain conformal, concave and/or separate air volumes, allowing simulation pattern. users to reduce the size of the FEM solution region resulting in a significant reduction in the solution time and the amount of memory required to solve the problem. C. FEKO FEKO is a comprehensive electromagnetic software suite (now part of Altair’s HyperWorks CAE simulation software platform), which includes many frequency and time domain solvers to solve a wide set of problems, involving complex materials and electrically large objects. FEKO has two sets of methods (full-wave methods and asymptotic methods), which are also hybridized to take profit from the advantages of both. The method used for this problem is FEKO’s MLFMM, which was included in FEKO in 2004. Alternatively, and to cross- validate the results, one could also use for this problem domain Fig. 5. CST Simulated E-field @10.7GHz (Left) and @18GHz (Right). decomposition: first using MLFMM for the feeder and Reflector SR 40-A with SH4000 Dual Ridge Horn. afterwards use such results as source while modelling the reflector with Physical Optics (PO). The currents induced on IV. COMPARISON RESULTS the antenna structure and the mesh grid used @ 18GHz are The simulations, based on different numerical methods are shown in Fig. 4. generally in very good agreement when compared to each other. The agreement between simulation and measurements is also considered excellent when considering uncertainties due to measurement and manufacturing. In the following, comparisons including the peak directivity, patterns, equivalent error level and losses are reported. A. Peak directivity comparison The peak directivity values are reported for measurements and simulations in TABLE II. The table confirms the very good agreement between measurements and simulations.

TABLE II. MEASURED AND SIMULATED PEAK DIRECTIVITY Fig. 4. FEKO currents induced on the antenna structure and applied mesh @18GHz on the Reflector SR 40-A with SH4000 Dual Ridge Horn. Peak Directivity [dBi] Currents (Left); Close-up of the feed (Right). Frequency Meas CST FEKO GRASP HFSS D. CST STUDIO SUITE (CST ) 10.7 GHz 30.99 30.96 31.11 31.09 31.04 CST offers several numerical simulation methods which 18 GHz 35.30 35.69 35.56 35.59 35.53 are very efficient for reflector design. Given the frequencies B. Pattern comparison and the electrical size of the reflector (24 λ x 28 λ @ 18 GHz) , The co-polar and cross-polar components at four patterns all the provided results have been obtained in a single cuts, phi=0°, 45°, 90° and 135° @ 10.7GHz and 18GHz are simulation run using the Time Domain Solver based on the compared with measurements in Fig. 6 to Fig. 13. MEAS is the Finite Integration Technique (FIT). Perfect Boundary measured reference as the mean of three measurements Approximation (PBA) is used for the spatial discretization of performed at UPM and MVG. The simulated results are from the structure. The simulated structure and the electromagnetic GRASP, FEKO, CST and HFSS. fields are mapped to a hexahedral mesh. PBA allows a very The agreement between simulation and measurements in good approximation of even curved surfaces within the cubic the plots is good especially considering that simulation results mesh cells. The obtained E-field for the present have been plotted with 0.1° angular step, while the step for [email protected] and 18GHz is shown in Fig. 5. measurements is 1°. The results can be cross-checked using a hybrid approach The agreement can also be evaluated as a single value. The in which an equivalent NF source from measurements or pattern correlation or equivalent noise level [3] is reported in generated by a time domain simulation of the horn antenna can the following paragraph. _._•=!•=•—.___ A A / \ I J AA s Al I 1 i A/^ ° /\ A A /\i ft ytt 1Í 11IV li * \ i \M>M*W\IM rill I víl ^ \/^^f I 1

Theta H Fig. 6. Reflector SR 40-A with SH4000: measured and simulated Fig. 10. Reflector SR 40-A with SH4000: measured and simulated (FEKO, CST, GRASP, HFSS) directivity pattern @10.7GHz, phi=0°. (FEKO, CST, GRASP, HFSS) directivity pattern @18GHz, phi=0°.

Fig. 7. Reflector SR 40-A with SH4000: measured and simulated Fig. 11. Reflector SR 40-A with SH4000: measured and simulated (FEKO, CST, GRASP, HFSS) directivity pattern @10.7GHz, phi=45°. (FEKO, CST, GRASP, HFSS) directivity pattern @18GHz, phi=45°.

SR40 + SH4000 Polar V / Directivity pattern @ phi=90° / 10700 MHz

3 r 1 N 7 u ' J'~\ / >, H V r> , : ,„. '.; ,. 1 1 /;'\ / ,'X' !,r\'i )Ú'V^)¡\ ; ;*/}/"\ 1 Theta (") Fig. 8. Reflector SR 40-A with SH4000: measured and simulated Fig. 12. Reflector SR 40-A with SH4000: measured and simulated (FEKO, CST, GRASP, HFSS) directivity pattern @10.7GHz, phi=90°. (FEKO, CST, GRASP, HFSS) directivity pattern @18GHz, phi=90°.

Fig. 9. Reflector SR 40-A with SH4000: measured and simulated Fig. 13. Reflector SR 40-A with SH4000: measured and simulated (FEKO, CST, GRASP, HFSS) directivity pattern @10.7GHz, phi=135°. (FEKO, CST, GRASP, HFSS) directivity pattern @18GHz, phi=135°. C. Pattern Correlation / Equivalent Noise Level V. CONCLUSIONS The visible pattern agreement is confirmed by computing The achievable agreement between antenna measurement the pattern correlation or equivalent noise level [3]. Correlation and numerical simulation has been investigated. The of simulation and measurement has been computed in a ±20° experiment has been designed to minimize error sources not conical angle for both polarizations as reported in TABLE III. pertinent to simulation/measurement. Correlation values of ~40dB are similar to what has been The simulations, based on different numerical methods are achieved in recent measurement comparisons [3]. generally in very good agreement when compared to each TABLE III. EQUIVALENT NOISE [email protected] AND 18 GHZ other. The agreement between simulation and measurements is deemed excellent, considering uncertainties due to simulation, Equivalent Noise Level wrt Measurements [dB] @10.7 GHz measurement and manufacturing. The level of correlation CST FEKO GRASP HFSS Phi between measurements and simulation achieved here are better CO CX CO CX CO CX CO CX than what has been found in recent facility comparisons 0° -42.52 -48.20 -42.07 -48.09 -43.57 -48.86 -44.05 -48.47 campaigns. Very good agreement has been achieved for 90° -44.08 -43.24 -42.41 -43.86 -43.91 -43.22 -44.73 -43.38 performance parameters such as peak directivity, pattern, and Equivalent Noise Level wrt Measurements [dB]@18 GHz gain contributions such as dissipation loss and matching. CST FEKO GRASP HFSS Phi CO CX CO CX CO CX CO CX REFERENCES 0° -41.61 -42.70 -41.74 -44.94 -41.47 -44.84 -43.12 -44.40 [I] ANSI/IEEE Std 149-1979, “Standard Test Procedures for Antennas” 90° -39.18 -42.33 -40.57 -42.36 -40.21 -42.22 -40.56 -42.29 [2] IEEE Std 1720 2012, “Recommended Practice for Near Field Antenna D. Dissipation Loss Comparison Measurements”. [3] L. J. Foged, M. Sierra Castañer, L. Scialacqua “Facility Comparison The measured and simulated dissipation losses are reported Campaigns within EurAAP”, 5th European conference on Antennas and in TABLE IV. Measured losses are obtained as the difference propagation, EuCAP2011, Rome, April 2011. between the IEEE Gain and the Directivity, therefore the [4] www.cst.com, CST STUDIO SUITE™, CST AG, Germany accuracy is related to the gain accuracy of the measurement [5] www.feko.info, Altair Engineering GmbH, Germany facilities. 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